Cycle LDPC code[1]
Description
An LDPC code whose parity-check matrix forms the incidence matrix of a graph, i.e., has weight-two columns.Protection
The minimum distance of a cycle LDPC code is \(d\geq g/2\), where \(g\) is the girth of the code's Tanner graph [2; Remark 21.2.13].Rate
Cycle codes are not asymptotically good [3].Encoding
Linear-time encoder [4].Realizations
Cycle LDPC codes have been proposed to be used for MIMO channels [5].Primary Hierarchy
Low-density parity-check (LDPC) code\(q\)-ary LDPC Tanner Linear \(q\)-ary LRC Distributed-storage ECC
Parents
Cycle LDPC codes form a class of regular QC LDPC codes [6].
Regular LDPC code\(q\)-ary LDPC Tanner Linear \(q\)-ary Linear code over \(\mathbb{Z}_q\) LRC Distributed-storage ECC
Cycle LDPC codes form a class of regular QC LDPC codes [6].
Cycle LDPC code
Children
Margulis LDPC codes are examples of cycle codes for particular large-girth graphs [7].
References
- [1]
- S. Hakimi and J. Bredeson, “Graph theoretic error-correcting codes”, IEEE Transactions on Information Theory 14, 584 (1968) DOI
- [2]
- C. A. Kelley, "Codes over Graphs." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021) DOI
- [3]
- L. Decreusefond and G. Zemor, “On the error-correcting capabilities of cycle codes of graphs”, Proceedings of 1994 IEEE International Symposium on Information Theory 307 DOI
- [4]
- Jie Huang and Jinkang Zhu, “Linear time encoding of cycle GF(2/sup P)/ codes through graph analysis”, IEEE Communications Letters 10, 369 (2006) DOI
- [5]
- Ronghui Peng and Rong-Rong Chen, “Application of Nonbinary LDPC Cycle Codes to MIMO Channels”, IEEE Transactions on Wireless Communications 7, 2020 (2008) DOI
- [6]
- R. M. Tanner, D. Sridhara, A. Sridharan, T. E. Fuja, and D. J. Costello, “LDPC Block and Convolutional Codes Based on Circulant Matrices”, IEEE Transactions on Information Theory 50, 2966 (2004) DOI
- [7]
- G. Zémor, “On Cayley Graphs, Surface Codes, and the Limits of Homological Coding for Quantum Error Correction”, Lecture Notes in Computer Science 259 (2009) DOI
Page edit log
- Fengxing Zhu (2024-03-16) — most recent
- Victor V. Albert (2024-03-16)
- Victor V. Albert (2023-05-09)
Cite as:
“Cycle LDPC code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/cycle_ldpc